I know B and G go pretty much hand in hand, one of the few differences being speed. My question is can a B network adapter always connect to a G network? If not, when can and can't it connect?

Generally，G network has three wireless mode , they are only-b, b&g and only-g.If only-b or b&g mode is configed in G network , b network adapter can connect to it, but if only-G wireless mode is set in G network, b network adapter can't connect it.Because B adapter does not support the basic-rate of only-G mode . Basic-rate of only-G mode includes 6Mpbs,12Mpbs,24Mpbs . B network adapter cannot demodulate the frame which is send from only-G network.
sorry for my English . I hope you can understand what I said.
thanks.